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by Maxatar 714 days ago
That is the specific bound. The little o is a function that aproaches 0 as n approaches infinity, referred to as asymptotically negligible.
1 comments

I know what the notation means. I'm wondering what the actual function is. Using little o is a way of abstracting that information away.
I could be wrong but I think many times the researchers don't care about the exact function. It could be something like 1/log(log(n)) .
Yes, I am very aware that many times they don't, but that doesn't mean they shouldn't!

Fortunately, in many cases, even when the detail is omitted from the headline theorem, they did in fact do the work and it is in fact stated lower down in the body of the paper; or in other cases they fail to state it but it can be easily assembled from a few parts. That's why I was asking.

But sometimes though it's a big complicated thing and they were just like, eh, let's not bother figuring out exactly what it is. To which I say, laziness! You're just making other people do a proof-mine later! You're doing this much, do the work to get a concrete bound, because you can do it better than later proof-miners can!

I won't say that in an ideally functioning mathematics proof-mining would never be necessary, that'd be like saying that in a well-written mathematics one would never need to refactor, but c'mon, mathematicians should at least do what they can to reduce the necessity of it.